• Ocean Systems Engineering
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• 제10권2호
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• pp.201-226
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• 2020

A systematic numerical comparative study of the performance of semicircular and rectangular submerged breakwaters interacting with solitary waves is the basis of this paper. To accomplish this task, Nwogu's extended Boussinesq model equations are employed to simulate the interaction of the wave with breakwaters. The finite difference technique has been used to discretize the spatial terms while a fourth-order predictor-corrector method is employed for time discretization in our numerical model. The proposed computational scheme uses a staggered-grid system where the first-order spatial derivatives have been discretized with fourth-order accuracy. For validation purposes, five test cases are considered and numerical results have been successfully compared with the existing analytical and experimental results. The performances of the rectangular and semicircular breakwaters have been examined in terms of the wave reflection, transmission, and dissipation coefficients (RTD coefficients) denoted by K_R, K_T, K_D. The latter coefficient K_D emerges due to the non-energy conserving K_R and K_T. Our computational results and graphical illustrations show that the rectangular breakwater has higher reflection coefficients than semicircular breakwater for a fixed crest height, but as the wave height increases, the two reflection coefficients approach each other. un the other hand, the rectangular breakwater has larger dissipation coefficients compared to that of the semicircular breakwater and the difference between them increases as the height of the crest increases. However, the transmission coefficient for the semicircular breakwater is greater than that of the rectangular breakwater and the difference in their transmission coefficients increases with the crest height. Quantitatively, for rectangular breakwaters the reflection coefficients K_R are 5-15% higher while the diffusion coefficients K_D are 3-23% higher than that for the semicircular breakwaters, respectively. The transmission coefficients K_T for rectangular breakwater shows the better performance up to 2.47% than that for the semicircular breakwaters. Based on our computational results, one may conclude that the rectangular breakwater has a better overall performance than the semicircular breakwater. Although the model equations are non-dissipative, the non-energy conserving transmission and reflection coefficients due to wave-breakwater interactions lead to dissipation type contribution.

• Ocean Systems Engineering
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• 제11권1호
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• pp.83-97
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• 2021

The submerged U-shape breakwater interaction with the solitary wave is simulated by the Boussinesq equations using the finite-difference scheme. The wave reflection, transmission, and dissipation (RTD) coefficients are used to investigate the U-shape breakwater's performance for different crest width, Lc1, and indent breakwater height, du. The results show that the submerged breakwater performance for a set of U-shape breakwater with the same cross-section area is related to the length of submerged breakwater crest, Lc1, and the distance between the crests, Lc2 (or the height of du). The breakwater has the maximum performance when the crest length is larger, and at the same time, the distance between them increases. Changing the Lc1 and du of the U-shape breakwaters result in a significant change in the RTD coefficients. Comparison of the U-shape breakwater, having the best performance, with the averaged RTD values shows that the transmission coefficients, Kt, has a better performance of up to 4% in comparison to other breakwaters. Also, the reflection coefficients KR and the diffusion coefficients, Kd shows a better performance of about 30% and 55% on average, respectively. However, the model governing equations are non-dissipative. The non-energy conserving of the transmission and reflection coefficients due to wave and breakwater interaction results in dissipation type contribution. The U-shape breakwater with the best performance is compared with the rectangular breakwater with the same cross-section area to investigate the economic advantages of the U-shape breakwater. The transmission coefficients, Kt, of the U-shape breakwater shows a better performance of 5% higher than the rectangular one. The reflection coefficient, KR, is 60% lower for U-shape in comparison to rectangular one; however, the diffusion coefficients, Kd, of U-shape breakwater is 35% higher than the rectangular breakwater. Therefore, we could say that the U-shape breakwater has a better performance than the rectangular one.

• 한국수자원학회논문집
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• 제44권6호
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• pp.471-476
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• 2011

In this study, a modified dispersion-correction scheme describing tsunami propagation on variable water depths is proposed by introducing additional terms to the previous numerical scheme. The governing equations used in previous tsunami propagation models are slightly modified to consider the effects of a bottom slope. The numerical dispersion of the proposed model replaces the physical dispersion of the governing equations. Then, the modified scheme is employed to simulate tsunami propagation on variable water depths and numerical results are compared with those of the previous tsunami propagation model.

• Korean Chemical Engineering Research
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• 제57권5호
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• pp.723-729
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• 2019

A theoretical analysis was conducted of convective instability driven by buoyancy forces under transient temperature fields in an annular porous medium bounded by coaxial vertical cylinders. Darcy's law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The linear stability equations are derived in a global domain, and then cast into in a self-similar domain. Using a spectral expansion method, the stability equations are reformed as a system of ordinary differential equations and solved analytically and numerically. The critical Darcy-Rayleigh number is founded as a function of the radius ratio. Also, the onset time and corresponding wavelength are obtained for the various cases. The critical time becomes smaller with increasing the Darcy-Rayleigh number and follows the asymptotic relation derived in the infinite horizontal porous layer.

• 한국어업기술학회:학술대회논문집
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• 한국어업기술학회 2000년도 추계수산관련학회 공동학술대회발표요지집
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• pp.167-168
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• 2000

A North Pacific Ocean Model has been developed with the Global Ocean Model of the Meteorological Research Institute of Japan which solves the primitive equations with Boussinesq, rigid-lid, and hydrostatic assumptions. The objective of the study is to improve the description of the variability on the East Sea and northwestern Pacific Ocean. (omitted)

• 대한조선학회지
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• 제24권2호
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• pp.55-61
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• 1987

The wave system due to a moving submerged body is investigated both theoretically and numerically. Boussinesq equation, which is derived under the assumption that the effects of nonlinearity and wave dispersion are of the same order, is generalized to take the forcing agency into account. Furthermore, under the more restrive assumption that the disturbance is of higher order, inhomogeneous Korteweg-de Vries equation is derived. These equations are solved numerically to obtain the generated wave system and the wave-making resistance. These results are compared with those given by the linear theory.

• 한국해안해양공학회지
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• 제17권1호
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• pp.1-8
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• 2005

지진해일을 수치모의할 때 임의로 구성된 유한요소망과 양해법을 사용하면서도 Boussinesq 방정식과 같은 정도의 물리적 분산효과를 고려할 수 있는 능동적인 분산보정 2차원 유한요소모형을 개발하였다. 새로운 기법을 이용하여 계산한 수치해와 파의 분산효과를 고려한 해석해의 비교를 통해 본 연구에서 개발한 분산보정기법의 타당성을 입증하였다. 그 결과 개발된 수치모형이 상당히 정확함을 보였다.

• 한국항해항만학회지
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• 제30권2호
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• pp.125-130
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• 2006

Waves, which are the main source of ship motions in a seaway, considerably affect the performance of a ship. The study of waves and their impact on ship motions within harbors is an important aspect of the design and operation of harbors. The prediction of incoming groups of waves is particularly important for evaluating ship motion within a harbor. Such a prediction makes it possible to evaluate ship safety more accurately. The wave transformation model reported here is applied to actual ports based on Boussinesq wave equations both non-linear and dispersive wave processes be considered in order to capture physical effects such as wave shoaling, refractions, reflection and diffraction in variable depth environments. The prediction of incoming groups of waves is particularly important for evaluating ship motion within a harbor, Such a prediction makes it possible to evaluate ship safety more accurately and provide safe wave informations for navigation. Furthermore, a wave information support system is proposed for entering ships as one technique for improving the safety of ship operations. This system predicts the run of waves and reduces the danger by identifying the most dangerous point near the harbor entrance at the small wave groups.

• 한국수자원학회논문집
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• 제45권6호
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• pp.545-555
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• 2012

컴퓨터 기술의 발달과 더불어 수치해석을 이용한 파랑변형에 대한 연구는 꾸준히 발전하고 있으며 점점 중요한 역할을 수행하고 있다. 하지만 수치모형을 이용한 연구에는 다양한 문제점이 발생할 우려가 있는데, 그 중 가장 빈번하게 발생하는 문제 중의 하나가 파랑의 조파지점에서 발생하는 수치수조내로의 재반사 문제이다. 재반사를 막기 위한 방법으로는 내부조파 기법을 이용하는 것이 일반적이다. Navier-Stokes 방정식 모형에서는 질량 원천항을 이용한 내부조파 기법을 주로 사용해 왔으나, 기존의 연구는 대부분 연직 2차원 수치모형을 이용한 연구에 국한되어 있었다. 그러나 3차원 수치모형을 이용한 연구가 점차 활발해지면서 3차원 Navier-Stokes 방정식 모형의 내부조파 기법에 대한 필요성이 증대되고 있다. 최근 RANS(Reynolds averaged Navier-Stokes) 방정식 모형에서 Boussinesq 방정식의 운동량 원천항을 활용하여 파랑을 내부조파하는 기법이 발표되어 3차원 공간에서 경사지게 입사하는 파랑을 성공적으로 재현하였다. 본 연구에서는 LES(large eddy simulation) 기반의 3차원 Navier-Stokes 방정식 수치모형에 운동량 원천항을 이용한 내부조파 기법을 적용하여 목표파랑을 조파하고 해석해와 비교하여 이를 검증하였다.

• 설비공학논문집
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• 제10권2호
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• pp.217-226
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• 1998

A numerical study has been carried out for two- and three-dimensional buoyant turbulent flow in a stairwell model. The Reynolds-averaged Navier-Stokes and energy equations are solved with the authors'own computer program. Two models by the Boussinesq approximation and the density-gradient form are used for buoyancy terms in the governing equations. Two- and three-dimensional predictions of the velocity and temperature fields are presented and the results are compared with experimental data. Comparisons have also been made in detail with two-dimensional predictions. Two-dimensional and three-dimensional simulations have predicted the overall features of the flow satisfactorily. A better agreement with experiment is achieved with three-dimensional simulations.